Knowing the time of onset of disease is usually crucial to understanding its etiology. However, in many epidemiologic studies, particularly those in which periodic screening is employed for ascertaining disease, only the interval in which disease began is known, but not the precise time of its onset. This event time is therefore interval-censored. The proposed research aims to develop the appropriate statistical methodology to deal with this common but little-appreciated problem of interval censorship. The investigators plan to develop statistical models for interval censored data that incorporate the pattern of examination times, the disease status at these assessments and concomitant information. Based on these models and by building on the work of the investigators and that of others in the analyses of right censored survival data, methods of estimation of, and making inference from, the distribution of the time of onset of disease will be developed. This will extend the limited published work available on methods for analyzing interval censored data. Computational algorithms for implementing these methods will be studied. As a supplementary aid to theoretical investigations, extensive computer simulation studies will be undertaken to compare and contrast the performance of these nonparametric estimation procedures with alternative schemes that make apriori parametric assumptions on the form of the underlying distribution of the event time, and imputation methods that use surrogate values for the missing times, such as the midpoint of the interval or the time of event diagnosis. Data from three large epidemiologic and clinical surveillance studies will be utilized to illustrate the proposed techniques and the results, assumptions and interpretations carefully compared with other methods. Bootstrap studies will be used to assess the stability of estimates. Preliminary work with one of these data sets describing brain hemorrhage in low birthweight infants indicates that estimating the time of onset of hemorrhage from interval-censored cranial ultrasound scanning data can provide illuminating insights into causation.